Beyond the Kibble-Zurek mechanism --- Universal distribution of topological defects created across a phase transition

Nonequilibrium phenomena occupy a prominent role at the frontiers of physics. Since its conception in the mid-70s, the Kibble-Zurek mechanism (KZM) has been the paradigmatic framework to describe the dynamics of phase transition, in which symmetry breaking leads to the formation of topological defects (e.g. vortices in a superfluid or kinks in a spin chain). Its key testable prediction is that the average number of topological defects scales as a universal power law with the quench rate (ie. the velocity at which the critical point is crossed). The authors unveil signatures of universality beyond the mean number of topological defects and show that the full counting statistics of topological defects is actually unanimous. In particular, the authors show that i) the defect number distribution is binomial, ii) all cumulants are proportional to the mean and scale as a universal power law with the quench rate, iii) this power law is fixed by the KZM scaling. This knowledge allows one to characterize universal features regarding the onset of adiabatic dynamics (probability for no defects) and large deviations of the number of kinks away from the mean value. This prediction is experimentally testable in the wide range of tangible platforms in which the KZM has been studied: trapped ion chains, liquid crystals, Bose-Einstein Condensate clouds, colloidal monolayers, to name just a few instances. The authors' findings provide a comprehensive set of predictions that can be subjected to extensive theoretical/numerical/experimental verification and apply to various disciplines and experimental systems.